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2 years ago

Can you help me on this

Mathematics

1 answer:

grigory [225]2 years ago

7 0

Answer:

The answers are x < -65, x > 85, x < 180, x<= -13, and x >=25.

Step-by-step explanation:

For the first three, there's an open circle so the sign for the inequality would be < or > but for the last two, there's a closed circle so the sign for the inequality would be <= or >=, the ones with a line underneath. For 1, 3, and 4, the line goes to the left, showing that x is a number less than the point so it would have <, the less than sign. For 2 and 5, the line goes to the right, showing that x is a number greater than the point so it would have >, the greater than sign.

There's a trick to figuring out the right sign. If the line is pointing to the left, the inequality would be x < __, and the sign is pointng to the left. If the line is pointing to the right, the inequality would be x > __, and the sign is pointng to the right. This only works is x is on the left side of the inequality.

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Simplify 1)5x+3=x+13 2)5/2x-1/X =1/6

Artyom0805 [142]

Step-by-step explanation (Question 1):

Step 1: (Question 1): Subtract x from both sides.

5x+3=x+13

5x+3−x=x+13−x

4x+3=13

Step 2: (Question 1): Subtract 3 from both sides.

4x+3−3=13−3

4x=10

Step 3: (Question 1): Divide both sides by 4.

4x/4 = 10/4

FIRST ANSWER: x = 5/2

Step-by-step explanation (Question 2):

Step 1: (Question 2): Multiply by LCM

15x^2 - 6 = x

Step 2: (Question 2): Solve 15x^2

15x^2 - 6 = x:

x = 2/3

x = -3/5

Step 3: (Question 2): Solve

ANSWER: x=0.666667 or x=−0.6

See Attachment 1 for question 1 steps (FULL)

See Attachment 2 for question 2 steps (FULL)

Answer:

1) x = 5/2

2) x=0.666667 or x=−0.6

Hope this helps.

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aivan3 [116]

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Step-by-step explanation:

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Ni is not correct. To solve the equivalent quarterly interest rate, the annual interest rate should be multiplied by the correct ratio. Since the annual interest rate is 4% per year. So in 1 quarter is equal to 0.25 year.

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3 years ago

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zvonat [6]

Answer:

24. see below for a drawing with axis intercepts labeled

30. the plane is parallel to the y-z plane. It is "x=4". The only axis intercept is (4, 0, 0).

Step-by-step explanation:

24. The axis intercepts are fairly easily found. You can do it a couple of ways.

first way

Set other variables to zero and divide by the coefficient of the variable of interest.

For 3x +5y +15z = 15, the x-intercept can be found by setting y and z to zero. This gives ...

3x = 15

so, dividing by 3 tells you the x-intercept is ...

x = 15/3 = 5

Likewise, the y- and z-intercepts are, respectively, ...

y = 15/5 = 3

z = 15/15 = 1

So, the points where the plane crosses the axes are ...

(5, 0, 0), (0, 3, 0), (0, 0, 1) . . . . axes intercepts

second way

Divide by the constant on the right, and express all coefficients as denominators

Doing that gives ...

$\dfrac{3x+5y+15z}{15}=1\\\\\dfrac{x}{5}+\dfrac{y}{3}+\dfrac{z}{1}=1$

The denominators are the corresponding intercepts. (This is called the "intercept form" of the equation of the plane.)

From the above equation, we see the axis intercepts are ...

(5, 0, 0), (0, 3, 0), (0, 0, 1) . . . . same as above

Actually, the math for these two methods is virtually identical. The second way does it "all at once", so can take fewer steps. Effectively, you're doing the math of the "first way" and expressing the result in the denominator.

Please note that when a variable is missing, there is no intercept for that axis. That is, the plane is parallel to that axis. (In problem 30, for example, the y- and z-variables are missing. The plane x=4 is parallel to the y- and z-axes (the y-z plane).)

_____

In the first attached drawing, the x-axis is red, the y-axis is green, and the z-axis is blue. The labeling of the points is difficult to see, but the axes are a different (lighter) color behind the plane than in front of it. This plane forms a triangle in the first octant (x, y, z > 0).

In the second attached drawing, the x=0 plane is blue; the y=0 plane is green, and the z=0 plane is red. The plane of the equation is yellow. This figure better shows the triangle in the first octant.

3-D graph paper (isometric graph paper) grids are available with a web search. Such might make it easier to draw the planes you need to draw. (See the third attachment for one example.)

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